A very good analysis. My only complaint with it is that a lot of it is conjecture based on the theory that the money supply is currently being increased, which is not actually the case. The Fed is not printing money, and in fact is not capable of doing so. It might be a very good idea right now, for reasons you are quite eloquent about, but the agency that would have to do it would be the Treasury, not the Fed.
The basic situation is that we went through very nasty credit-induced recession. We don't know what's typical for such things really, but the last one is now called "The Great Depression", and took more than a decade (and some say a major war) to recover from. So we should be thankful things aren't far worse, but they still suck compared to a typical "recovery". There's a good chance it will recover on its own eventually, but for us humans "eventually" doesn't buy us groceries, so it would be a really good idea to do what we reasonably can to help it.
The problem there is that we are currently the proud holders of a congress that couldn't pass gas in a chili house. The political cynic in me would say that the Republican Congress doesn't want the economy to recover before the 2018 election, and is doing everything they can to stop recovery efforts. But even if you don't buy that, its undeniable that there's no way they are going to allow any further stimulus (that isn't war-related).
So this means that the Treasury department will simply not be allowed to print money to help us out of this, no matter how good of an idea it may seem. The only government agencies that are capable of acting are independent agencies, and of those the only one with a mission of looking after the economy is The Fed. They can't print money of course, but what they can do is effectively give free loans to banks (which they are doing), and take treasury securities out of circulation by increasing reserve requirements (which they are also doing). Both of these in theory ought to make it easier and more attractive for banks to give out loans and people to buy stocks.
Of course this means that those who don't want the economy stimulated now hate the Fed, and are spewing all kinds of vitrol against it. It doesn't matter much if there's any truth in their complaints, because what the Fed actually does is so arcane that nobody can refute lies without making the typical American's eyes glaze over.